The Pluses and Minuses of +/-

The validity of plus/minus has been debated frequently here at Raptors Republic with several misconceptions around both “basic/raw” and “adjusted” measures.

The NBA posts raw +/- scores here. A few days ago, it was noted the DeMar DeRozan had the worst plus/minus in the league – what does this mean?. And how is it that Andrea Bargnani can have 23 points with a -21 rating one night and 25 points and +29 the very next game?!

So, what is this measure and why is it (or not) important?
“Raw”, “Basic” or “Simple” plus/minus is what you see in the NBA box scores.

It’s simply the difference between points scored (+) as a team versus points allowed (-) while that player is on the floor.

Why is it good?
In theory, it measures the player’s total impact on the floor. While the focus for many looking a the box score is “how many points did player x get?”, this metric attempts to capture his ultimate influence on the outcome of the game – did player x leave the game with the team scoring more than the opponent?

What are the issues with it?
The primary one is it doesn’t account for the “environment”. Does the player usually play with good or poor teammates? Does he usually play against the opponent’s starters? Bench? or Garbage time?

To illustrate:
Carlos Arroyo has a +/- of +144. Deron Williams? “Only” +44
So is Arroyo a better player? Let’s look at his “environment”

Arroyo has played ~600 minutes with ALL of Wade, Bosh, and James on the floor with him.
Williams has played the most minutes (779) with the “big three” of Kirilenko, Jefferson, and Millsap.

It’s quite clear that Arroyo’s +/- is driven by simply being on the floor with three of the best in the league.

How are the Raptors players doing?

Given our record (and our 24th ranked efficiency differential), it’s no surprise the majority of our players are in negative territory. Only Joey Dorsey and Julian Wright are in positive territory. Given they have limited minutes under their belts and they have often played against the opponent’s second units, its hard to draw any conclusions. It’s also not a surprise that Bargnani, DeRozan and Evans have the worst +/- given they’ve played the most starting minutes – thus against the opponent’s best lineups.

What can we conclude about “raw” +/-? Not to rely on it. Game by game and even over the course of the season, it’s hazardous to draw firm conclusions from “good” or “bad” +/- scores.

A better metric – “adjusted” plus/minus

Several people know I am a big fan of this metric. It’s foundations go back to Dan T. Rosenbaum’s work in 2004. Aaron Barzilai runs a site that I use very often – basketballvalue.com – which updates these values on a nightly basis.

Here’s why I’m a fan: Mr. Rosebaum developed adjusted +/- to attempt to address these questions:

Good players lead their teams to wins. Lots of players can fill up a stat sheet, but only the great ones are difference-makers. The objective of a basketball game is not to accumulate points or rebounds or assists, but to win. What statistic do you have for that?

So what is it? How is it measured?

Adjusted +/- ratings indicate how many additional points are contributed to a team’s scoring margin by a given player in comparison to the league-average player over the span of a typical game (100 offensive and defensive possessions). – Aaron Barzilai, Ph.D. and Steve Ilardi, Ph.D.

To put in simple terms, it adjusts the raw/basic +/- to factor in the quality of players that a given player plays with and against.

Let’s go back to our previous example between Carlos Arroyo and Deron Williams. What does the Adjusted +/- statistic say?

Does this seem more consistent with their abilities? It appears so.

How much should we rely on it to rate players?

It is important to note that the adjusted +/- rating is not a “holy grail” statistic that perfectly captures each player’s overall value. – Barzilai and Ilardi.

The authors properly warn about large standard errors unless a large sample size is used – noting that even a full season is often inadequate (we most often focus on the two year metric for this reason). It also suffers from skewed sampling: “it can be difficult to accurately tease out the individual effects of two players who almost always appear on the court together.”

Certainly there are anomalies due to these issues, but don’t most measures have problems as well? Should we rank players simply by PPG, ignoring the efficiency of which they get those points as well as their impact on defense?

Why do I like it? It’s a great tool to screen players and start “filling in the blanks”. For example, last year Amir Johnson screened well. He’s still at the top of all Raptors for 2 year adjusted +/-. If nothing else, you start asking questions: “does he really impact the game in a positive way?” “Well, he doesn’t score much, but he’s efficient.” “Hmm, he’s one of the top offensive rebounders per minute (second chance points!)”. “He fouls a ton, but some of that is due to help defense – no easy baskets.” “He runs the floor well creating easier opportunities for himself and teammates.” “His hustle may just inspire teammates to play a little harder on D”. Etc.. You don’t have to agree, but these metrics get us thinking on what might explain the data and if there’s something to it or not.

This is also why I was pushing for Julian Wright early on. His 2 year adjusted +/- is generally 1st or 2nd along with Johnson. And by watching the games, you could see – despite some offensive limitations – he was making a difference: hunting down loose balls, drawing charges, sticking to his man, making nice passes, etc. What’s happened when he plays more? One stat: in the three games that he’s played more than 21 minutes he’s averaged approximately 7 pts, 6 rbs, and a +14 rating. ALL were wins on the road (two against good teams). Bundle this data together, watch some tape and we should conclude that its worth playing him more to either: confirm if our analysis is correct or this is all just a fluke. It’s worth a test.